November 2001 - Course 1 SOA Solutions

3. A
Since
3 4 2 5
S = 175L A , we have
∂ S
1 4
=
2 5
262.5 L A > 0 for
∂L
L > 0 , A > 0
2
∂ S
− 1 4
2 5
= 131.25 L A > 0 for
2
∂L
L> 0 , A>
0
∂ S
3 −1 = 140 L 2
A 5 > 0 for
∂A
L > 0 , A > 0
2
∂ S
3 −6
2 5
=− 28 L A < 0 for
2
∂A
L> 0 , A>
0
It follows that S increases at an increasing rate as L increases, while S increases at a
decreasing rate as A increases.
4. B
Apply Baye’s Formula:
Pr ⎡⎣Seri. Surv. ⎤⎦
=
Pr ⎡⎣Surv. Seri. ⎤⎦Pr[ Seri. ]
Pr ⎡⎣Surv. Crit. ⎤ ⎦Pr[ Crit. ] + Pr ⎡⎣Surv. Seri. ⎤ ⎦Pr[ Seri. ] + Pr ⎡⎣Surv. Stab. ⎤⎦Pr[ Stab. ]
( 0.9)( 0.3)
0.29
( 0.6)( 0.1) + ( 0.9)( 0.3) + ( 0.99)( 0.6)
= =
Course 1 Solutions 2 November 2001